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3

Does it have to be open source? If I wanted to make a FPS my first choice would be UDK. It's what it does best (and not much more).
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DiegoOct 9 '11 at 12:10

3

Why exactly the 'Lua' constrain? It would help us to give you a better suggestion.
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iamcreasyOct 9 '11 at 15:00

2

Best with regards to what: rendering quality, hardware compatibility, highest fps rates, most consistent fps rates, ease of use? What kind of environment does the action take place: indoor, urban, outdoors? Do you need a physics engine, what will you use it for (racing, flying, or good-looking explosions)? What about sound? For competitive first-person shooters, directional sound and the ability to control attenuation is important. You need to be more precise about your goals and constraints.
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JohDec 31 '11 at 10:01

Plugin development tutorial for integrating Lua scripting with Crystal Space Engine. But, I would suggest to stay away form this engine.

BlendElf is a good choice.But, I don't think the developer is continuously working on it any more. Once I asked him why he isn't using QT or other gui lib for Editor development, he answered it is a showcase project, that's why. argh! You should also notice that the last forum activity is May, 2011. Bad sign.

If you see Horde 3d feature list, you will see Strong modularity and high abstraction through flat C-style DLL API (also makes it possible to use Horde3D from virtually any programming language), just like Leadwerks Engine.

If you are not satisfied yet, GPWiki & DevMaster have a huge list of game engines and scripting feature is specified there. Many well/less known engines has Lua with it. Check it out.

The Blender Game Engine is pretty good for 3D games. It doesn't use Lua, but it uses Python, which is more comfortable to me (objects, classes, inheritance). It can definitely do FPS games, and supports GLSL shading. It also has the Bullet physics engine included, and, of course, is present inside of the 3D modeler, Blender.

Well, that pretty much leaves Ogre, although frankly it isn't a game engine, it's a renderer/scenegraph. You still need to plug in the other bits like IO, physics and audio, but plenty of options already exist.

If you drop the Lua requirement, your options open up a heck of a lot more, as does if you drop the Open Source requirement.